The shape of the variable plates for Straight-Line Capacitance, Straight-Line Wavelength and Straight-Line Frequency air variable capacitors are shown pictorial in the Radio Engineering book by Terman, 1937, 2nd ed., page 30.

(1) Instead of the above traditional design, what would the shape of the straight-line frequency air variable plates look like if they were flat plates in the horizontal plane sliding over each other? i.e. A brass plate sliding over another brass plate separated by glass, cardboard or air on top of my work bench.

For practice the stator plate could be taped horizontally flat to the work bench and the rotor plate could be taped to a piece of cardboard and also laid flat on top of the work bench. This flat rotor could be pushed over the fixed stator to change capacitance.

What shape should these two flat plates look like to act as an straight-line frequency air variable capacitor?

The shape is going to be a smooth curve, something like a parabola,rather than a straight line.

To get an exact Straight Line Frequency (SLF) you have to know the tuningrange and the fixed (minimum) circuit capacitance. The commercial SLFcapacitors are typically designed for tuning the broadcast band, andwill only give SLF behavior over about a 3 : 1 frequency range.

The bottom plate can be the same shape as the upper one, or can be a rectangle or any other shape, as long as it extends at least as far as the upper plate. (Assuming the upper plate is the one that is shapedto provide the specified tuning rate.)

Let's take an example: assume we want to tune 3.5 - 4 MHz and thefixed minimum capacitance in the circuit is 50pf.

At 4 MHz we have only the 50pf fixed capacitor in the circuit, so theinductance must be 31.66uH. Based on that we can calculate theadditional capacitance required for each 100kHz increment:

3.9 MHz needs 52.6 pf, for a delta of 2.6pf3.8 MHz needs 55.4 pf, for a delta of 2.8pf3.7 MHz needs 58.4 pf, for a delta of 3pf3.6 MHz needs 61.7 pf, for a delta of 3.3pf3.5 MHz needs 65.3pf, for a delta of 3.6pf

Since the delta isn't constant, you can't use a plate with straight edges.However, if you break the tuning range into small enough steps you cancalculate the plate size for each based on straight lines between stepsand get pretty close.

Or you can derive the shape mathematically by calculating a curve withthe proper integral to give the tuning function, but that would take morethought than I can give it at the moment.

Slice a non-curving trumpet in half. That general 'shape' slid onto a plate, pointy end first, will yield a 'linear' increase in capacitance. There's a geometrical description for that sort of 'curve', damned if I can remember what the name of it is, way too long since I was out of school. - 'Doc

To get SLF characteristic, you need a capacitance, which for given mechanical delta, has a square law characteristic of area, since f is proportional to C squared. It won't be a hyperbola, but it will be cam shaped and there should be somewhere a way to figure this shape out. More math than I care to do.....

But it won't be straight line, because a straight line is y=mx+c, where m is the slope and c is a constant. Differentiating gives the delta as always equal to m.

With zero stray capacitance (the simple 'ideal' case) you get SLC by sliding two rectangular plates.

SLW (wavelength) comes from a triangular plate, as overlap area varies as the square of the displacement.

SLF requires some stray capacitance; without this you get 'infinite frequency' with no overlap. Given the strays, some algebra then gives the required overlap area variation with displacement. Calculus (differentiation) then gives the required shape.

You can find the capacitance formula for two flat plates in any physics book. the dielectric is a multiplier.I think glass is around a "2".I don't know how linear it would be , but it is simple enough to make one and try it.

Slice a non-curving trumpet in half. That general 'shape' slid onto a plate, pointy end first, will yield a 'linear' increase in capacitance. There's a geometrical description for that sort of 'curve', damned if I can remember what the name of it is, way too long since I was out of school.

W9GB,Certainly could be! It was quite a while ago when I saw an example of the shape and it wasn't talking about exactly the same thing. This was well before computer simulation came along so there are bound to be 'differences' or exceptions to what's accepted now. Oh well, some of that 'old' stuff is still worth remembering at times. - Paul

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